Theorems · Theorem · group theory
Group.nilpotencyClass_quotient_center
∀ {G : Type u_1} [inst : Group G], Group.nilpotencyClass (G ⧸ Subgroup.center G) = Group.nilpotencyClass G - 1Quotienting the center G reduces the nilpotency class by 1.
- Defined in
- Mathlib.GroupTheory.Nilpotent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- le_antisymmproof · cited by 2,068
- le_of_eqproof · cited by 366
- add_tsub_cancel_rightproof · cited by 172
- Subgroup.comapproof · cited by 154
- Subgroup.centerstatement and proof · cited by 121
- zero_tsubproof · cited by 100
- QuotientGroup.mk'proof · cited by 90
- Group.IsNilpotentproof · cited by 80
Cited by3
Results whose statement or proof uses this declaration.
- Group.nilpotent_center_quotient_indproof · cited by 2
- Group.nilpotencyClass_eq_quotient_center_plus_oneproof · cited by 1
- nilpotencyClass_quotient_centerproof · cited by 0